IB GEOMETRY BIBLE - POSTULATES 1

PostulatesPostulatesPostulatesPostulates

Postulate 1 (Ruler Postulate)Postulate 1 (Ruler Postulate)Postulate 1 (Ruler Postulate)Postulate 1 (Ruler Postulate) 1. The points on a line can be paired with the real numbers in such a way that any

two points can have coordinates 0 and 1. 2. Once a coordinate system has been chosen in this way, the distance between

any two points equals the absolute value of the difference of their coordinates.

Postulate 2 (Segment Addition Postulate)Postulate 2 (Segment Addition Postulate)Postulate 2 (Segment Addition Postulate)Postulate 2 (Segment Addition Postulate) If B is between A and C, then AB + BC = AC. Postulate 3 (Protractor Postulate)Postulate 3 (Protractor Postulate)Postulate 3 (Protractor Postulate)Postulate 3 (Protractor Postulate)

On AB in a given plane, choose any point O between A and B. Consider OA and OB and all the rays that can be drawn from 0 on one side of AB. These rays can be paired with the real numbers from 0 to 180 in such a way that: a.a.a.a. OA is paired with 0, and OB with 180.

b.b.b.b. If OP is paired with x, and OQ with y, then m∠POQ = | x – y |. Postulate 4 (Angle Addition Postulate)Postulate 4 (Angle Addition Postulate)Postulate 4 (Angle Addition Postulate)Postulate 4 (Angle Addition Postulate)

If point B lies in the interior of ∠AOC, then m∠AOC, then m∠AOC + m∠BOC = m∠AOC.

If ∠AOC is a straight angle and B is any point not on AC, then m∠AOB + m∠BOC = 180. Postulate 5Postulate 5Postulate 5Postulate 5 A line contains at least two points; a plane contains at least three points not all in one line; space contains at least four points not all in one plane. Postulate 6Postulate 6Postulate 6Postulate 6 Through any two points there is exactly one line. Postulate 7Postulate 7Postulate 7Postulate 7 Through any three points there is at least one plane, and through any three noncollinear points there is exactly one plane. Postulate 8Postulate 8Postulate 8Postulate 8 If two points are in a plane, then the line that contains the points is in that plane. Postulate 9Postulate 9Postulate 9Postulate 9 If two planes intersect, then their intersection is a line.

IB GEOMETRY BIBLE - POSTULATES 2

PostulaPostulaPostulaPostulate 10te 10te 10te 10 If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel. Postulate 11Postulate 11Postulate 11Postulate 11 If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel. Postulate 12Postulate 12Postulate 12Postulate 12 (SSS Pos (SSS Pos (SSS Pos (SSS Postulate)tulate)tulate)tulate) If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. Postulate 1Postulate 1Postulate 1Postulate 13 (SAS Postulate)3 (SAS Postulate)3 (SAS Postulate)3 (SAS Postulate) If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent. Postulate 1Postulate 1Postulate 1Postulate 14 (ASA Postulate)4 (ASA Postulate)4 (ASA Postulate)4 (ASA Postulate) If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. Postulate Postulate Postulate Postulate 15 (15 (15 (15 (AA Similarity Postulate)AA Similarity Postulate)AA Similarity Postulate)AA Similarity Postulate) If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. Postulate 1Postulate 1Postulate 1Postulate 16 (Arc Addition Postulate)6 (Arc Addition Postulate)6 (Arc Addition Postulate)6 (Arc Addition Postulate) The measure of the arc formed by two adjacent arcs is the sum of the measure of those two arcs. Postulate 1Postulate 1Postulate 1Postulate 17 7 7 7 The area of a square is the length of a side. (A = s2) Postulate 1Postulate 1Postulate 1Postulate 18 (Area Congruence Postulate)8 (Area Congruence Postulate)8 (Area Congruence Postulate)8 (Area Congruence Postulate) If two figures are congruent, then they have the same area. Postulate 1Postulate 1Postulate 1Postulate 19 (Area Addition Postulate)9 (Area Addition Postulate)9 (Area Addition Postulate)9 (Area Addition Postulate) The area of a region is the sum of the areas of its non-overlapping parts.